SOLUTION: Determine the sum to 16 terms of the arithmetic series whose 7th term is 19 and whose 10th term is 25

Question 1068733: Determine the sum to 16 terms of the arithmetic series whose 7th term is 19 and whose 10th term is 25
Answer by swincher4391(1107) (Show Source): You can put this solution on YOUR website!
Since we are told that we have an arithmetic series, that means there is a common difference between terms. Call it "d".
So, first let's find what that common difference is.

We are told that the 7th term is 19
And that the 10th term is 25.
So we are adding the common difference to get from the 7th to 8th, 8th to 9th, 9th to 10th. Or a total of 3 times.
So 19 + 3d = 25
3d = 6
So d = 2.
Now let's find the 1st term. We are told that the 7th term is 19, so we add the common difference 6 times from the 1st term.
or A_1 + (7-1)*2 = 19
A_1 + 12 = 19
A_1 = 7
So we know the common difference =2, the first term is 7, and we know the number of terms we are adding.
We still need to know the last term. So the last term can be found by taking a_10 + (6-1)*2 = 25 + 10 = 35
The sum is:
number of terms*(1st term + last term)/2
16*(7+35)/2 =

RELATED QUESTIONS
Find the arithmetic series whose 6th term is 0 and whose 10th term is 16. Show that there (answered by ewatrrr)

Find the 10th term of a series in Arithmetic series, whose sum to n terms is 3n+4n2(4 n... (answered by solver91311)

Calculate the first ten term of an arithmetic progression whose 5th term is 24 and the... (answered by Edwin McCravy,MathTherapy)

Determine the sum of the first 15 terms of the arithmetic series whose 5th term is 4 and... (answered by ikleyn)

find the sum of the arithmetic series whose first term is 52, whose last term is 12 and... (answered by ewatrrr)

Find the 10th term of an arithmetic sequence whose 5th term is 1.25 and whose 15th term... (answered by ikleyn)

Find the 10th term of an arithmetic sequence whose 5th term is 1.25 and whose 15th term... (answered by Fombitz)

the 5th term in a geometric progression is 9 times the 3rd term and the sum of the 6th... (answered by Boreal,ikleyn)

the 7th term of an AP is 19 and the 8th term is 22.find the sum of the first 40th terms... (answered by Boreal)